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The filling radius function R of Gromov measures the minimal radii of van Kampen diagrams filling edge-circuits w in the Cayley 2-complex of a finite presentation P. It is known that the Dehn function...
Alexander varieties and largeness of finitely presented groups
Alexander varieties largeness of finitely presented groups Group Theory
2012/5/9
Let X be a finite CW complex. We show that the fundamental group of X is large if and only if there is a finite cover Y of X and a sequence of finite abelian covers \{Y_N\} of Y which satisfy b_1(Y_N)...
The computational complexity of recognising embeddings in finitely presented groups
Finitely presented groups embeddings Kleene’s arithmetical hierarchy decidability universal finitely presented group
2011/8/29
Abstract: We extend a result by Lempp that recognising torsion-freeness for finitely presented groups is $\Pi^{0}_{2}$-complete; we show that the problem of recognising embeddings of finitely presente...
Some Properties of Finitely Presented Groups with Topological Viewpoints
Finitely presented group Fundamental group Homotopy group
2011/1/19
In this paper, using some properties of fundamental groups and covering spaces of connected polyhedra and CW-complexes, we present topological proof for some famous theorems about finitely presented g...
Spectral triples for finitely presented groups, index 1
Spectral triples finitely presented groups
2010/11/23
Using generalized Cayley graphs and Clifford algebras, we are able to give, for a large class of finitely presented groups, a uniform construction of spectral triples with $D_{+}$ of index $1$.